Bull. Korean Math. Soc. 2020; 57(2): 489-508
Online first article August 2, 2019 Printed March 31, 2020
https://doi.org/10.4134/BKMS.b190357
Copyright © The Korean Mathematical Society.
Xin Si, Ce Xu
Xiamen University of Technology; Xiamen University
This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polylogarithms. By using the approach, we establish some relations between quadratic Euler sums and linear sums. Furthermore, we obtain some closed form representations of quadratic sums in terms of zeta values and linear sums. The given representations are new.
Keywords: Harmonic numbers, polylogarithm function, Euler sum, Riemann zeta function
MSC numbers: Primary 11M06, 11M32, 33B15
Supported by: This work was co-supported by the National Natural Science Foundation of China (No.41801219), Natural Science Foundation of Fujian Province (No.2019J01849).
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